Title of article :
The Sum of a Linear and a Linear Fractional Function: Pseudoconvexity on the Nonnegative Orthant and Solution Methods
Author/Authors :
MARTEIN, LAURA University of Pisa - Department of Statistics and Applied Mathematics, Italy , CAROSI, LAURA University of Pisa - Department of Statistics and Applied Mathematics, Italy
Abstract :
The aim of the paper is to present sequential methods for a pseudoconvex optimization problem whose objective function is the sum of a linear and a linear fractional function and the feasible region is a polyhedron, not necessarily compact. Since the sum of a linear and a linear fractional function is not in general pseudoconvex, we first derive conditions characterizing its pseudoconvexity on the nonnegative orthant. We prove that the sum of a linear and a linear fractional function is pseudoconvex if and only if it assumes particular canonical forms. Then, theoretical properties regarding the existence of a minimum point and its location are established, together with necessary and sufficient conditions for the infimum to be finite. The obtained results allow us to suggest simplex-like sequential methods for solving optimization problems having as objective function the proposed canonical forms.
Keywords :
Pseudoconvexity , fractional programming
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society